scholarly journals Absolute continuity of the spectrum of multidimensional periodic magnetic Dirac operator

2008 ◽  
pp. 61-96 ◽  
Author(s):  
L.I. Danilov ◽  
Keyword(s):  
Dirac Operator ◽  
Absolute Continuity ◽  
Continuity Of The Spectrum

scholarly journals Absolute continuity of the spectrum in a twisted Dirichlet-Neumann waveguide

2020 ◽  
Vol 61 (1) ◽  
pp. 013503
Author(s):  
Ph. Briet ◽  
J. Dittrich ◽  
D. Krejčiřík
Keyword(s):  
Absolute Continuity ◽  
Continuity Of The Spectrum

scholarly journals Decay rates at infinity for solutions to periodic Schrödinger equations

2019 ◽  
Vol 150 (3) ◽  
pp. 1113-1126
Author(s):  
Daniel M. Elton
Keyword(s):  
Half Space ◽  
Absolute Continuity ◽  
Evolution Equations ◽  
Schrödinger Operators ◽  
Decay Rates ◽  
Schrodinger Equations ◽  
Schrodinger Operators ◽  
Schrödinger Equations ◽  
The Absolute ◽  
Continuity Of The Spectrum

AbstractWe consider the equation Δu = Vu in the half-space ${\open R}_ + ^d $, d ⩾ 2 where V has certain periodicity properties. In particular, we show that such equations cannot have non-trivial superexponentially decaying solutions. As an application this leads to a new proof for the absolute continuity of the spectrum of particular periodic Schrödinger operators. The equation Δu = Vu is studied as part of a broader class of elliptic evolution equations.

scholarly journals Commutator methods for the spectral analysis of uniquely ergodic dynamical systems

2014 ◽  
Vol 35 (3) ◽  
pp. 944-967 ◽  
Author(s):  
R. TIEDRA DE ALDECOA
Keyword(s):  
Spectral Analysis ◽  
Dynamical Systems ◽  
Absolute Continuity ◽  
Unitary Operators ◽  
Skew Products ◽  
Lebesgue Spectrum ◽  
The Absolute ◽  
Time Changes ◽  
Continuity Of The Spectrum ◽  
Uniquely Ergodic

AbstractWe present a method, based on commutator methods, for the spectral analysis of uniquely ergodic dynamical systems. When applicable, it leads to the absolute continuity of the spectrum of the corresponding unitary operators. As an illustration, we consider time changes of horocycle flows, skew products over translations and Furstenberg transformations. For time changes of horocycle flows we obtain absolute continuity under assumptions weaker than those to be found in the literature, and for skew products over translations and Furstenberg transformations we obtain countable Lebesgue spectrum under assumptions not previously covered in the literature.

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